In this paper, we present the results of searching the Kepler Q2 public data set for the secondary eclipses of 76 hot Jupiter planet candidates from the list of 1235 candidates published by Borucki et al., 2011, Cat. J/ApJ/736/19. This search has been performed by modeling both the Kepler pre-search data conditioned light curves and new light curves produced via our own photometric pipeline. We derive new stellar and planetary parameters for each system, while calculating robust errors for both. We find 16 systems with 1{sigma}-2{sigma}, 14 systems with 2{sigma}-3{sigma}, and 6 systems with >3{sigma} confidence level secondary eclipse detections in at least one light curve produced via the Kepler pre-search data conditioned light curve or our own pipeline; however, results can vary depending on the light curve modeled and whether eccentricity is allowed to vary or not. We estimate false alarm probabilities of 31%, 10%, and 6% for the 1{sigma}-2{sigma}, 2{sigma}-3{sigma}, and >3{sigma} confidence intervals, respectively.